Sum of Cantor sets: Self-similarity and measure
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- by Pedro Mendes PDF
- Proc. Amer. Math. Soc. 127 (1999), 3305-3308 Request permission
Abstract:
In this note it is shown that the sum of two homogeneous Cantor sets is often a uniformly contracting self-similar set and it is given a sufficient condition for such a set to be of Lebesgue measure zero (in fact, of Hausdorff dimension less than one and positive Hausdorff measure at this dimension).References
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Additional Information
- Pedro Mendes
- Affiliation: Departamento de Matemática, ICEx, UFMG Av. Antonio Carlos 6627 31270.901 Belo Horizonte, MG, Brazil
- Email: pmendes@mat.ufmg.br
- Received by editor(s): February 6, 1998
- Published electronically: May 13, 1999
- Communicated by: Michael Handel
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 3305-3308
- MSC (1991): Primary 28A78, 58F14
- DOI: https://doi.org/10.1090/S0002-9939-99-05107-2
- MathSciNet review: 1637408